qiskit.quantum_info.DensityMatrix¶

class
DensityMatrix
(data, dims=None)[소스]¶ DensityMatrix class
Initialize a density matrix object.
 매개변수
(np.ndarray or list or matrix_like or QuantumCircuit or (data) – qiskit.circuit.Instruction): A statevector, quantum instruction or an object with a
to_operator
orto_matrix
method from which the density matrix can be constructed. If a vector the density matrix is constructed as the projector of that vector. If a quantum instruction, the density matrix is constructed by assuming all qubits are initialized in the zero state.dims (int or tuple or list) – Optional. The subsystem dimension of the state (See additional information).
 예외
QiskitError – if input data is not valid.
 Additional Information:
The
dims
kwarg can be None, an integer, or an iterable of integers.Iterable
– the subsystem dimensions are the values in the list with the total number of subsystems given by the length of the list.Int
orNone
– the leading dimension of the input matrix specifies the total dimension of the density matrix. If it is a power of two the state will be initialized as an Nqubit state. If it is not a power of two the state will have a single ddimensional subsystem.

__init__
(data, dims=None)[소스]¶ Initialize a density matrix object.
 매개변수
(np.ndarray or list or matrix_like or QuantumCircuit or (data) – qiskit.circuit.Instruction): A statevector, quantum instruction or an object with a
to_operator
orto_matrix
method from which the density matrix can be constructed. If a vector the density matrix is constructed as the projector of that vector. If a quantum instruction, the density matrix is constructed by assuming all qubits are initialized in the zero state.dims (int or tuple or list) – Optional. The subsystem dimension of the state (See additional information).
 예외
QiskitError – if input data is not valid.
 Additional Information:
The
dims
kwarg can be None, an integer, or an iterable of integers.Iterable
– the subsystem dimensions are the values in the list with the total number of subsystems given by the length of the list.Int
orNone
– the leading dimension of the input matrix specifies the total dimension of the density matrix. If it is a power of two the state will be initialized as an Nqubit state. If it is not a power of two the state will have a single ddimensional subsystem.
Methods
__init__
(data[, dims])Initialize a density matrix object.
Return the conjugate of the density matrix.
copy
()Make a copy of current operator.
dims
([qargs])Return tuple of input dimension for specified subsystems.
draw
([output])Return a visualization of the Statevector.
evolve
(other[, qargs])Evolve a quantum state by an operator.
expand
(other)Return the tensor product state other ⊗ self.
expectation_value
(oper[, qargs])Compute the expectation value of an operator.
from_instruction
(instruction)Return the output density matrix of an instruction.
from_int
(i, dims)Return a computational basis state density matrix.
from_label
(label)Return a tensor product of Pauli X,Y,Z eigenstates.
is_valid
([atol, rtol])Return True if trace 1 and positive semidefinite.
measure
([qargs])Measure subsystems and return outcome and postmeasure state.
probabilities
([qargs, decimals])Return the subsystem measurement probability vector.
probabilities_dict
([qargs, decimals])Return the subsystem measurement probability dictionary.
purity
()Return the purity of the quantum state.
reset
([qargs])Reset state or subsystems to the 0state.
Return a DensityMatrix with reversed subsystem ordering.
sample_counts
(shots[, qargs])Sample a dict of qubit measurement outcomes in the computational basis.
sample_memory
(shots[, qargs])Sample a list of qubit measurement outcomes in the computational basis.
seed
([value])Set the seed for the quantum state RNG.
tensor
(other)Return the tensor product state self ⊗ other.
to_dict
([decimals])Convert the density matrix to dictionary form.
Convert to Operator
to_statevector
([atol, rtol])Return a statevector from a pure density matrix.
trace
()Return the trace of the density matrix.
Attributes
Default absolute tolerance parameter for float comparisons.
Return data.
Return total state dimension.
Return the number of qubits if a Nqubit state or None otherwise.
Default relative tolerance parameter for float comparisons.

property
atol
¶ Default absolute tolerance parameter for float comparisons.

copy
()¶ Make a copy of current operator.

property
data
¶ Return data.

property
dim
¶ Return total state dimension.

dims
(qargs=None)¶ Return tuple of input dimension for specified subsystems.

draw
(output=None, **drawer_args)[소스]¶ Return a visualization of the Statevector.
repr: ASCII TextMatrix of the state’s
__repr__
.text: ASCII TextMatrix that can be printed in the console.
latex: An IPython Latex object for displaying in Jupyter Notebooks.
latex_source: Raw, uncompiled ASCII source to generate array using LaTeX.
qsphere: Matplotlib figure, rendering of density matrix using plot_state_qsphere().
hinton: Matplotlib figure, rendering of density matrix using plot_state_hinton().
bloch: Matplotlib figure, rendering of density matrix using plot_bloch_multivector().
 매개변수
output (str) – Select the output method to use for drawing the state. Valid choices are repr, text, latex, latex_source, qsphere, hinton, or bloch. Default is repr. Default can be changed by adding the line
state_drawer = <default>
to~/.qiskit/settings.conf
under[default]
.drawer_args – Arguments to be passed directly to the relevant drawing function or constructor (TextMatrix(), array_to_latex(), plot_state_qsphere(), plot_state_hinton() or plot_bloch_multivector()). See the relevant function under qiskit.visualization for that function’s documentation.
 반환값
matplotlib.Figure
orstr
orTextMatrix
orIPython.display.Latex
: Drawing of the Statevector. 예외
ValueError – when an invalid output method is selected.

evolve
(other, qargs=None)[소스]¶ Evolve a quantum state by an operator.
 매개변수
(Operator or QuantumChannel (other) – or Instruction or Circuit): The operator to evolve by.
qargs (list) – a list of QuantumState subsystem positions to apply the operator on.
 반환값
the output quantum state.
 반환 형식
QuantumState
 예외
QiskitError – if the operator dimension does not match the specified QuantumState subsystem dimensions.

expand
(other)[소스]¶ Return the tensor product state other ⊗ self.
 매개변수
other (DensityMatrix) – a quantum state object.
 반환값
the tensor product state other ⊗ self.
 반환 형식
 예외
QiskitError – if other is not a quantum state.

expectation_value
(oper, qargs=None)[소스]¶ Compute the expectation value of an operator.
 매개변수
oper (Operator) – an operator to evaluate expval.
qargs (None or list) – subsystems to apply the operator on.
 반환값
the expectation value.
 반환 형식
complex

classmethod
from_instruction
(instruction)[소스]¶ Return the output density matrix of an instruction.
The statevector is initialized in the state \({0,\ldots,0}\rangle\) of the same number of qubits as the input instruction or circuit, evolved by the input instruction, and the output statevector returned.
 매개변수
instruction (qiskit.circuit.Instruction or QuantumCircuit) – instruction or circuit
 반환값
the final density matrix.
 반환 형식
 예외
QiskitError – if the instruction contains invalid instructions for density matrix simulation.

static
from_int
(i, dims)[소스]¶ Return a computational basis state density matrix.
 매개변수
i (int) – the basis state element.
dims (int or tuple or list) – The subsystem dimensions of the statevector (See additional information).
 반환값
The computational basis state \(i\rangle\!\langle i\).
 반환 형식
 Additional Information:
The
dims
kwarg can be an integer or an iterable of integers.Iterable
– the subsystem dimensions are the values in the list with the total number of subsystems given by the length of the list.Int
– the integer specifies the total dimension of the state. If it is a power of two the state will be initialized as an Nqubit state. If it is not a power of two the state will have a single ddimensional subsystem.

classmethod
from_label
(label)[소스]¶ Return a tensor product of Pauli X,Y,Z eigenstates.
¶ Label
Statevector
"0"
\(\begin{pmatrix} 1 & 0 \\ 0 & 0 \end{pmatrix}\)
"1"
\(\begin{pmatrix} 0 & 0 \\ 0 & 1 \end{pmatrix}\)
"+"
\(\frac{1}{2}\begin{pmatrix} 1 & 1 \\ 1 & 1 \end{pmatrix}\)
""
\(\frac{1}{2}\begin{pmatrix} 1 & 1 \\ 1 & 1 \end{pmatrix}\)
"r"
\(\frac{1}{2}\begin{pmatrix} 1 & i \\ i & 1 \end{pmatrix}\)
"l"
\(\frac{1}{2}\begin{pmatrix} 1 & i \\ i & 1 \end{pmatrix}\)
 매개변수
label (string) – a eigenstate string ket label (see table for allowed values).
 반환값
The Nqubit basis state density matrix.
 반환 형식
 예외
QiskitError – if the label contains invalid characters, or the length of the label is larger than an explicitly specified num_qubits.

measure
(qargs=None)¶ Measure subsystems and return outcome and postmeasure state.
Note that this function uses the QuantumStates internal random number generator for sampling the measurement outcome. The RNG seed can be set using the
seed()
method. 매개변수
qargs (list or None) – subsystems to sample measurements for, if None sample measurement of all subsystems (Default: None).
 반환값
 the pair
(outcome, state)
whereoutcome
is the measurement outcome string label, and
state
is the collapsed postmeasurement state for the corresponding outcome.
 the pair
 반환 형식
tuple

property
num_qubits
¶ Return the number of qubits if a Nqubit state or None otherwise.

probabilities
(qargs=None, decimals=None)[소스]¶ Return the subsystem measurement probability vector.
Measurement probabilities are with respect to measurement in the computation (diagonal) basis.
 매개변수
qargs (None or list) – subsystems to return probabilities for, if None return for all subsystems (Default: None).
decimals (None or int) – the number of decimal places to round values. If None no rounding is done (Default: None).
 반환값
The Numpy vector array of probabilities.
 반환 형식
np.array
예제
Consider a 2qubit product state \(\rho=\rho_1\otimes\rho_0\) with \(\rho_1=+\rangle\!\langle+\), \(\rho_0=0\rangle\!\langle0\).
from qiskit.quantum_info import DensityMatrix rho = DensityMatrix.from_label('+0') # Probabilities for measuring both qubits probs = rho.probabilities() print('probs: {}'.format(probs)) # Probabilities for measuring only qubit0 probs_qubit_0 = rho.probabilities([0]) print('Qubit0 probs: {}'.format(probs_qubit_0)) # Probabilities for measuring only qubit1 probs_qubit_1 = rho.probabilities([1]) print('Qubit1 probs: {}'.format(probs_qubit_1))
probs: [0.5 0. 0.5 0. ] Qubit0 probs: [1. 0.] Qubit1 probs: [0.5 0.5]
We can also permute the order of qubits in the
qargs
list to change the qubit position in the probabilities outputfrom qiskit.quantum_info import DensityMatrix rho = DensityMatrix.from_label('+0') # Probabilities for measuring both qubits probs = rho.probabilities([0, 1]) print('probs: {}'.format(probs)) # Probabilities for measuring both qubits # but swapping qubits 0 and 1 in output probs_swapped = rho.probabilities([1, 0]) print('Swapped probs: {}'.format(probs_swapped))
probs: [0.5 0. 0.5 0. ] Swapped probs: [0.5 0.5 0. 0. ]

probabilities_dict
(qargs=None, decimals=None)¶ Return the subsystem measurement probability dictionary.
Measurement probabilities are with respect to measurement in the computation (diagonal) basis.
This dictionary representation uses a Ketlike notation where the dictionary keys are qudit strings for the subsystem basis vectors. If any subsystem has a dimension greater than 10 comma delimiters are inserted between integers so that subsystems can be distinguished.
 매개변수
qargs (None or list) – subsystems to return probabilities for, if None return for all subsystems (Default: None).
decimals (None or int) – the number of decimal places to round values. If None no rounding is done (Default: None).
 반환값
The measurement probabilities in dict (ket) form.
 반환 형식
dict

reset
(qargs=None)[소스]¶ Reset state or subsystems to the 0state.
 매개변수
qargs (list or None) – subsystems to reset, if None all subsystems will be reset to their 0state (Default: None).
 반환값
the reset state.
 반환 형식
 Additional Information:
If all subsystems are reset this will return the ground state on all subsystems. If only a some subsystems are reset this function will perform evolution by the reset
SuperOp
of the reset subsystems.

reverse_qargs
()[소스]¶ Return a DensityMatrix with reversed subsystem ordering.
For a tensor product state this is equivalent to reversing the order of tensor product subsystems. For a density matrix \(\rho = \rho_{n1} \otimes ... \otimes \rho_0\) the returned state will be \(\rho_0 \otimes ... \otimes \rho_{n1}\).
 반환값
the state with reversed subsystem order.
 반환 형식

property
rtol
¶ Default relative tolerance parameter for float comparisons.

sample_counts
(shots, qargs=None)¶ Sample a dict of qubit measurement outcomes in the computational basis.
 매개변수
shots (int) – number of samples to generate.
qargs (None or list) – subsystems to sample measurements for, if None sample measurement of all subsystems (Default: None).
 반환값
sampled counts dictionary.
 반환 형식
Additional Information:
This function samples measurement outcomes using the measure
probabilities()
for the current state and qargs. It does not actually implement the measurement so the current state is not modified.The seed for random number generator used for sampling can be set to a fixed value by using the stats
seed()
method.

sample_memory
(shots, qargs=None)¶ Sample a list of qubit measurement outcomes in the computational basis.
 매개변수
shots (int) – number of samples to generate.
qargs (None or list) – subsystems to sample measurements for, if None sample measurement of all subsystems (Default: None).
 반환값
list of sampled counts if the order sampled.
 반환 형식
np.array
Additional Information:
This function samples measurement outcomes using the measure
probabilities()
for the current state and qargs. It does not actually implement the measurement so the current state is not modified.The seed for random number generator used for sampling can be set to a fixed value by using the stats
seed()
method.

seed
(value=None)¶ Set the seed for the quantum state RNG.

tensor
(other)[소스]¶ Return the tensor product state self ⊗ other.
 매개변수
other (DensityMatrix) – a quantum state object.
 반환값
the tensor product operator self ⊗ other.
 반환 형식
 예외
QiskitError – if other is not a quantum state.

to_dict
(decimals=None)[소스]¶ Convert the density matrix to dictionary form.
This dictionary representation uses a Ketlike notation where the dictionary keys are qudit strings for the subsystem basis vectors. If any subsystem has a dimension greater than 10 comma delimiters are inserted between integers so that subsystems can be distinguished.
 매개변수
decimals (None or int) – the number of decimal places to round values. If None no rounding is done (Default: None).
 반환값
the dictionary form of the DensityMatrix.
 반환 형식
dict
예제
The ketform of a 2qubit density matrix \(rho = \rangle\!\langle \otimes 0\rangle\!\langle 0\)
from qiskit.quantum_info import DensityMatrix rho = DensityMatrix.from_label('0') print(rho.to_dict())
{'0000': (0.4999999999999999+0j), '1000': (0.49999999999999990j), '0010': (0.4999999999999999+0j), '1010': (0.4999999999999999+0j)}
For nonqubit subsystems the integer range can go from 0 to 9. For example in a qutrit system
import numpy as np from qiskit.quantum_info import DensityMatrix mat = np.zeros((9, 9)) mat[0, 0] = 0.25 mat[3, 3] = 0.25 mat[6, 6] = 0.25 mat[1, 1] = 0.25 rho = DensityMatrix(mat, dims=(3, 3)) print(rho.to_dict())
{'0000': (0.25+0j), '1010': (0.25+0j), '2020': (0.25+0j), '2222': (0.25+0j)}
For large subsystem dimensions delimiters are required. The following example is for a 20dimensional system consisting of a qubit and 10dimensional qudit.
import numpy as np from qiskit.quantum_info import DensityMatrix mat = np.zeros((2 * 10, 2 * 10)) mat[0, 0] = 0.5 mat[1, 1] = 0.5 rho = DensityMatrix(mat, dims=(2, 10)) print(rho.to_dict())
{'0000': (0.5+0j), '9191': (0.5+0j)}

to_statevector
(atol=None, rtol=None)[소스]¶ Return a statevector from a pure density matrix.
 매개변수
atol (float) – Absolute tolerance for checking operation validity.
rtol (float) – Relative tolerance for checking operation validity.
 반환값
 The pure density matrix’s corresponding statevector.
Corresponds to the eigenvector of the only nonzero eigenvalue.
 반환 형식
 예외
QiskitError – if the state is not pure.